QUADRATIC EQUATIONSAlgebraTakingSquareRootA pure quadratic equation can be solved by taking the square root of both sides of the equation.Before taking the square root, the equation must be arranged with the x^{2} term isolated on the left-hand side of the equation and its coefficient reduced to 1. There are four steps in solving purequadratic equations by taking the square root.Step 1. Using the addition and subtraction axioms, isolatethe x^{2} term on the left-hand side of the equation.Step 2. Using the multiplication and division axioms,eliminate the coefficient from the x^{2}term.Step 3. Take the square root of both sides of the equation.Step 4. Check the roots.In taking the square root of both sides of the equation, there are two values that satisfy theequation. For example, the square roots of x^{2} are +x and -x since (+x)(+x) = x^{2} and(-x)(-x) = x^{2}. The square roots of 25 are +5 and -5 since (+5)(+5) = 25 and (-5)(-5) = 25. Thetwo square roots are sometimes indicated by the symbol ±. Thus, . Because of this25±5property of square roots, the two roots of a pure quadratic equation are the same except for theirsign.At this point, it should be mentioned that in some cases the result of solving pure quadraticequations is the square root of a negative number. Square roots of negative numbers are calledimaginary numbers and will be discussed later in this section.Example:Solve the following quadratic equation by taking the square roots of both sides.3x^{2} = 100 - x^{2}Solution:Step 1. Using the addition axiom, add x^{2} to both sides of the equation.3x^{2} + x^{2}= 100 - x^{2} + x^{2}4x^{2}= 100MA-02 Page 18 Rev. 0

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